Systems, methods, and structures for improved supercontinuum generation

ABSTRACT

Aspects of the present disclosure describe improved supercontinuum generation based upon alternating optical dispersion along a waveguide length that advantageously generates much more spectral bandwidth than possible with conventional, prior art techniques without losing coherence as well as supporting a larger range of pulse energies (i.e., for lower than conventionally allowed pulse energies or high pulse energies).

TECHNICAL FIELD

This disclosure relates generally to systems, methods, and structuresfor improved supercontinuum generation (SCG).

BACKGROUND

Recently, supercontinuum generation—a process by which laser light isconverted to light exhibiting a very broad spectral bandwidth, i.e., avery low temporal coherence and a super-wide continuous opticalspectrum—has become of great interest as such supercontinuum sourceshave found applicability in a wide array of important contemporaryapplications including medical diagnostics, environmentaldetection/analysis, light detection and ranging (LiDAR), and opticalcommunications such as via frequency combs—among others.

Given the utility, importance, and necessity of supercontinuumgeneration to such applications, systems, methods, and structures forimprove supercontinuum generation would represent a welcome addition tothe art.

SUMMARY

An advance in the art is made according to aspects of the presentdisclosure directed to systems, methods, and structures for improvedsupercontinuum generation that advantageously and repeatedly re-shapespulse(s) during, before or after nonlinear generation such that itmaintains an ideal temporal shape for enhanced spectral generation.

Advantageously, systems, methods, and structures according to thepresent disclosure increase the spectral bandwidth of SCG well beyondthose achieved in the art, while maintaining coherence in generation.

In sharp contrast to the prior art—instead of maintaining a spatiallyuniform or tapered waveguide dispersion along the propagationlength—systems, methods, and structures according to aspects of thepresent disclosure alternate the dispersion of a length of waveguide viachanging (alternating) segments of normal and anomalous dispersionwaveguide segments.

By configuring a chain of such alternating segments with an appropriatelength distribution, systems, methods, and structures according to thepresent disclosure advantageously and surprisingly impose alternatingtemporal focusing and defocusing thereby avoiding soliton formation,spectral narrowing, as well as loss of peak intensity, while self-phasemodulation increases the spectral bandwidth without undesirable spectralclamping.

BRIEF DESCRIPTION OF THE DRAWING

A more complete understanding of the present disclosure may be realizedby reference to the accompanying drawing in which:

FIG. 1(A) is a schematic diagram illustrating supercontinuum generationin a generic waveguide (e.g., integrated or fiber waveguide) having achain of segments of alternating normal dispersion (ND) and anomalousdispersion (AD) according to aspects of the present disclosure;

FIG. 1(B) is a plot illustrating broadening of an energy densityspectrum vs. propagating through a chain of AD and ND segments,calculated for the example of a transform-limited Gaussian input pulsewhen only first and second order dispersion is present according toaspects of the present disclosure;

FIG. 1(C) is a plot illustrating the temporal shape of an example pulseas in FIG. 1(B), calculated in a travelling frame vs. propagationcoordinate, accounting up to second order dispersion according toaspects of the present disclosure;

FIG. 2(A) is a plot showing the comparison of the spectral developmentin each ND segment along the propagation direction of the ND SCG chainwith an equivalent length case of just the ND waveguide whereindispersion is not present but nonlinearity remains and the equivalentlength case wherein there is only a continuous length of the ND materialwith both dispersion and nonlinearity. Note that the dispersion chosenis considered to be within a standard range for step-index fibers and isthus not a negligible value according to aspects of the presentdisclosure;

FIG. 2(B) is a plot showing the lower bound calculation for thebandwidth increase ratio between subsequent ND segments according toaspects of the present disclosure;

FIG. 2(C) is a plot showing the bandwidth increase ratio at the end ofeach ND segment (with respect to the previous segment) wherein the lowerbound calculation is shown and the ratio of the nonlinear to dispersionlength of at the start of each progressive ND segment is shown accordingto aspects of the present disclosure;

FIG. 3 is a schematic diagram illustrating an experimental setup forsupercontinuum generation according to aspects of the presentdisclosure;

FIG. 4 is a plot illustrating second-order dispersion vs. wavelength ofexperimentally used AD and ND fiber segments in which the verticaldotted lines indicate the zero dispersion wavelengths of the AD (1.31μm) and ND (1.83 μm) segments according to aspects of the presentdisclosure;

FIG. 5 is a plot illustrating measured power spectrum obtained fromsupercontinuum generation in a segmented chain fiber waveguide inwhich—for comparison—the measured spectra obtained with the same lengthof normally dispersive (ND) fiber and anomalous dispersion (AD) fiberare displayed as well as obtained with the same pulse input parameters,also a numerical simulation, according to aspects of the presentdisclosure;

FIG. 6(A) is a plot illustrating relative spectral energy density (dB)vs. wavelength (μm) for an output spectrum measured behind each NDsegment in the chain according to aspects of the present disclosure;

FIG. 6(B) is a plot illustrating relative pulse intensity (color coded)and temporal shape (Fs) vs. propagation distance (cm) vs. time (fs) inwhich the time coordinate is taken in a frame moving with group velocityaccording to aspects of the present disclosure; and

FIG. 7(A)-FIG. 7(E) are schematic diagrams of illustrative waveguideconfigurations providing SCG of optical pulses that may advantageouslyand illustratively implemented in integrated waveguide structuresemploying contemporary processes and materials according to aspects ofthe present disclosure in which: FIG. 7(A) is a first case illustrativeconfiguration; FIG. 7(B) is a second case illustrative configuration;FIG. 7(C) is a third case illustrative configuration; FIG. 7(D) showsillustrative parameters of waveguide structures; a plot illustratingrelative spectral energy density (dB) vs. wavelength (μm) for an outputspectrum measured behind each ND segment in the chain according toaspects of the present disclosure; FIG. 7(E) shows cross-sectional viewsof illustrative waveguides;—all according to aspects of the presentdisclosure.

The illustrative embodiments are described more fully by the Figures anddetailed description. Embodiments according to this disclosure may,however, be embodied in various forms and are not limited to specific orillustrative embodiments described in the drawing and detaileddescription.

DESCRIPTION

The following merely illustrates the principles of the disclosure. Itwill thus be appreciated that those skilled in the art will be able todevise various arrangements which, although not explicitly described orshown herein, embody the principles of the disclosure and are includedwithin its spirit and scope.

Furthermore, all examples and conditional language recited herein areintended to be only for pedagogical purposes to aid the reader inunderstanding the principles of the disclosure and the conceptscontributed by the inventor(s) to furthering the art and are to beconstrued as being without limitation to such specifically recitedexamples and conditions.

Moreover, all statements herein reciting principles, aspects, andembodiments of the disclosure, as well as specific examples thereof, areintended to encompass both structural and functional equivalentsthereof. Additionally, it is intended that such equivalents include bothcurrently known equivalents as well as equivalents developed in thefuture, i.e., any elements developed that perform the same function,regardless of structure.

Thus, for example, it will be appreciated by those skilled in the artthat any block diagrams herein represent conceptual views ofillustrative circuitry embodying the principles of the disclosure.

Unless otherwise explicitly specified herein, the FIGs comprising thedrawing are not drawn to scale.

As those skilled in the art will appreciate upon understanding ourdisclosure, we present a new approach to supercontinuum generation thatalternates the sign, and with it possibly also the shape and strength,of dispersion along a length of a waveguide. We demonstrate ourtechnique by showing a substantial bandwidth enhancement in a standard,step-index fiber including a chain of fiber segments configured suchthat dispersion alternates repeatedly between normal and anomalous. Aswe disclose, systems, methods and structures for supercontinuumgeneration—according to the present disclosure—are particularly wellsuited for integrated optical supercontinuum generation and the plethoraof applications that arise from such advancement.

We begin by noting supercontinuum generation (SCG) in waveguides is oneof the most intriguing phenomena in non-linear optics due to its uniquepotential for combining broad spectral bandwidth with high coherence andpower efficiency. Of particular interest and advantage, output may bespectrally centered in the mid-infrared to ultraviolet regions asdetermined by specific optical materials, waveguide dispersion, and pumplaser wavelength employed.

Contemporary SCG involves a single-pass nonlinear conversion in opticalfibers providing usually negative (anomalous) group velocity dispersion,possibly also positive (normal) group velocity dispersion. More recentlySC has been generated in integrated optical waveguides as well. Incertain resonant systems the same underlying phenomena form the basisfor broadband frequency comb generation (Kerr comb generation). In eachof these situations, achieving an output exhibiting a large bandwidthand high coherence is necessary when employing same in such applicationsas microwave photonics, sensing and precision metrology.

As those skilled in the art will understand and appreciate however,while the spectral bandwidth in SCG can reach even several hundreds ofTHz in specific cases while realizing a high conversion efficiency,ultimately, the bandwidth remains clamped, that is to say it cannotexceed a certain range without significant loss of coherence. Whenemploying anomalous dispersion—which is a common technique used inbroadband SCG—the process initially benefits from dispersive pulsecompression (temporal focusing), but spectral clamping is inherent tosubsequent soliton formation.

Beyond these limits, it is known that further broadening can be achievedvia employing Raman interaction, four-wave mixing and dispersive wave(DW) generation. Unfortunately, these processes generate eithernarrowband radiation (DW) or are prone to low coherence, e.g., due tothe influence of vacuum fluctuations, modulation instability, orstochastic soliton fission. And while solitons are not formed whenemploying normal dispersion in SCG, however, spectral clamping remainsinherent because pump pulses become temporally stretched (defocused) andlose their peak intensity with increasing propagation length.

Alternating Dispersion Supercontinuum Generation

Accordingly, we disclose and describe herein a novel approach forincreasing the spectral bandwidth of SCG—and surprisingly—well beyondnamed limits, while maintaining coherence in generation.

Such SCG is realized according to aspects of the present disclosure—insharp contrast to prior art techniques that generally maintain aspatially uniform or tapered waveguide dispersion along a propagationlength—by alternating the dispersion via changing waveguide segments ofnormal (ND segment) and anomalous dispersion (AD segment) as shownschematically in FIG. 1(A).

More specifically, FIG. 1(A) is a schematic diagram illustratingsupercontinuum generation in a generic waveguide (e.g., integrated orfiber waveguide) having a chain of segments of alternating normaldispersion (ND) and anomalous dispersion (AD) according to aspects ofthe present disclosure. Note that while the figure shows the ND segmentinitially preceding the AD segment, our disclosure is not so limited,and such will be disclosed and discussed in more detail subsequently.

FIG. 1(B) is a plot illustrating broadening of an energy densityspectrum vs. propagating through a chain of AD and ND segments,calculated for the example of a transform-limited Gaussian input pulsewhen only first and second order dispersion is present according toaspects of the present disclosure.

FIG. 1(C) is a plot illustrating the temporal shape of an example pulseas in FIG. 1(B), calculated in a travelling frame vs. propagationcoordinate, accounting up to second order dispersion according toaspects of the present disclosure.

With initial reference now to FIG. 1(A)—as noted—there is shown aschematic diagram illustrating a waveguide structure according toaspects of the present disclosure. As may be observed from that figure,a “chain” of waveguide segments is configured such that the segmentsalternate between normal dispersion (ND) segments and anomalousdispersion (AD) segments as one progresses along the overall waveguidelength. In the illustrative configuration shown, SPM spectral broadeningwill occur primarily in the ND segments.

At this point we note that as used herein, a waveguide is any structurethat guides waves, such as electromagnetic waves, with minimal loss ofenergy by restricting expansion to selected dimension(s). Of particularinterest to this disclosure—are optical waveguides that guideelectromagnetic waves in an optical portion of the electromagneticspectrum. Such optical waveguides include both optical fiber andrectangular as well as non-rectangular (i.e., integrated) waveguidesthat are constructed to be spatially inhomogeneous such that the spatialregion in which light propagates therein is restricted. As will be knownby those skilled in the art, such optical waveguides will include aregion exhibiting a different refractive index from surroundingregion(s).

We further note—with respect to the illustrative figures—that as shownillustratively is an ND segment as the first segment in the chain ofsegments. Those skilled in the art will know and appreciate that thecharacteristic of the first segment may be either ND or AD, so long asthe alternating characteristic along the length of the waveguidestructure is maintained. As we shall describe further, which particularsegment provides focusing and which provides defocusing will be a matterof design choice and configuration according to aspects of the presentdisclosure.

As we shall show and describe, systems, methods, and structuresemploying dielectric waveguides or more specifically planar opticalwaveguides may advantageously be employed according to the presentdisclosure. Such planar waveguide structures benefit significantly fromsilicon waveguide processing techniques, processes, and materials thatcontinue to advance at an accelerating pace.

Finally, with returning reference to FIG. 1(A), we note that by choosinga chain of such alternating segments exhibiting an appropriate lengthdistribution, we impose alternating temporal focusing and defocusingthat advantageously avoids both soliton formation as well as loss ofpeak intensity, while increasing self-phase modulation of spectralbandwidth without producing spectral clamping.

To illustratively demonstrate our approach, we show a bandwidthenhancement of SC generation in a dispersion segmented optical fiberchain configured according to aspects of the present disclosure. Notethat such demonstration is only illustrative and in no way limiting.

Those skilled in the art will readily understand and appreciate thatsalient effects of SCG important to our approach include self-phasemodulation (SPM), dispersion, and the dynamics resulting from theinterplay of these two effects. Via the intensity-dependent Kerr effect,SPM generates a coherent broadening in the spectral domain that dependson the peak intensity, pulse duration and propagation distance. Tomaximize spectral broadening by SPM, the pulse duration must beminimized, and the peak intensity maximized. However, in the presence ofAD, the temporal profile can shape itself into a soliton pulse, wherethe temporal chirp contributions of SPM become balanced with that ofdispersion. This has the effect of preventing further spectralbroadening, even though this pulse is at a minimal duration (i.e.,transform limited). Note further that with respect to an optical pulsein an AD waveguide—if no soliton is generated as a result ofinsufficient pulse energy—the pulse will first compress and then stretchwith a reversed temporal chirp, resulting in spectral clamping as withthe normal dispersion case.

Advantageously, with our approach according to aspects of the presentdisclosure, we prevent the occurrence of such “spectro-temporalstagnation” repeatedly, by alternating between ND and AD waveguidesegments along the propagation. Of further advantage, supercontinuumgeneration according to aspects of the present disclosure may beperformed at lower powers—and in particular—lower than necessary forsoliton generation. Accordingly, and as will be readily appreciated bythose skilled in the art, supercontinuum generation systems, methods,and structures according to the present disclosure operate in regimesthat cannot be used in conventional supercontinuum generation setups astaught and disclosed in the art.

Operationally, in sections of AD we perform temporal compression toincrease (maximize) the peak intensity, and to decrease (minimize) pulseduration such that SPM spectral broadening is always optimized for thesegment and/or the subsequent ND segment. However, before a soliton canform, we reverse the dispersion with a ND segment, such that coherentSPM spectral broadening remains ongoing, without termination throughsoliton formation or a broadened temporal profile.

Depending on the specific optical materials and geometries employed,spectral broadening through SPM will occur predominantly in ND segments,in AD segments, or in both—depending upon particular configuration. Fora basic illustration of the concept, we proceed only with the first casewhere the AD segments merely serve to temporally compress the opticalpulse to, ideally, the transform limit with only negligible nonlinearcontributions. SPM spectral broadening is maximized and carried out onlyin the ND segments. We label such a structure as an ND SCG chain. Ofcourse, such illustrating is in now way limiting as any of theabove-identified cases/scenarios are contemplated and included in thescope of the present disclosure.

Another reason for choosing this case as an illustrative example is thatit exhibits a spectral coherence advantage over the other case (withstrong SPM occurring in the AD segments). The reason is that modulationinstabilities (MI) are absent in ND SCG, which inhibits the growth ofnoise via MI.

Continuing with our illustrative discussion, we assume for specificitythat a transform limited Gaussian pulse serves as input into a first NDsegment as such a pulse is at its minimum duration, which maximizes SPMspectral broadening. As spectral broadening occurs, the pulseaccelerates its rate of temporal defocusing. This eventually results ina temporally stretched pulse having a much longer duration and lowerpeak intensity that inhibits SPM. At this point in its propagationthrough the segmented waveguide, the pulse enters an AD segment wherethe pulse becomes temporally re-focused to ideally its transform limit.

Temporally, the pulse can now maximize SPM and broadening in the next NDsegment relative to the case where it is temporally broadened. Thus,once the point of strongest temporal focusing is reached in the ADsegment, the cycle is repeated with a next ND segment for SPM spectralbroadening, then a next AD segment for temporal re-focusing and so on.Accordingly, spectral broadening can be increased in steps—towards adesired bandwidth—while circumventing spectral clamping through loss ofpeak intensity and increased pulse duration. The dynamics of the othercase (where SPM is non-negligible in the AD sections) is highly similarand according details are presented later.

Quantification of the ND SCG Case

In order to quantify the conditions that the lengths of the segmentsfulfill for inducing the described dynamics in a ND SCG chain, we recallthe basic relations describing nonlinearity and group velocitydispersion. Ideally, for large SPM spectral broadening in the NDsegments, the nonlinear length, L_(nl) ^((ND)), has to be smaller thanthe dispersion length, L_(D) ^((ND)), with

$L_{n\; l}^{({ND})} \equiv \frac{1}{\gamma^{({ND})}P_{o}} < L_{D}^{({ND})} \equiv {\frac{t_{o}^{2}}{\beta_{2}^{({ND})}}.}$

Here, t_(o) is the transform limited pulse duration (e⁻¹ intensity) atthe input of the ND (or AD) segment, P_(o) the input peak power, γ, isthe waveguide nonlinear coefficient, and β₂ ^((ND)) is group velocitydispersion in the ND segment. For the AD segments, γ^((AD))→0,minimizing bandwidth increase in the AD segments.

Those skilled in the art will appreciate that it can be seen from theabove relations that the dispersion length decreases quadratically withdecreasing transform limited pulse duration (i.e., with increasingspectral width) but the nonlinear length decreases linearly. Thus, inthe limit of many ND segments, when the spectrum has substantiallybroadened, L_(l) ^((ND)) will become greater or equal than L_(D)^((ND))—always. However, it will be shown both numerically and with ourexperimental results that substantial spectral broadening stilltranspires when L_(nl) ^((ND)) becomes larger or equal to L_(LD)^((ND)).

Note that while these lengths work for the idealized case of a Gaussianinput pulse with only up to second order dispersion, these lengthrelations are paramount in deriving relevant expressions needed tooptimize the SCG process in segmented waveguide chains with alternatingdispersion according to aspects of the present disclosure.

For example, the minimal spectral bandwidth increase obtained in each NDsegment of a ND SCG chain can be derived using the above showncharacteristic length relations and it can be shown to be increasingexponentially. This result is important—not only does this SCG methodaccording to aspects of the present disclosure bypass spectral clampingin dispersive media, the spectral bandwidth increases exponentially,meaning that the chain need not be composed of many segments for a largespectral enhancement and in general, shows that the chain is a powerfulsolution to generate SCG relative to conventional methods.

To further elaborate on the above, we note that the spectral bandwidthenclosed between the e⁻¹ spectral intensity values (Δω), increases ineach ND segment by at least a factor of √{square root over (2)},relative to the previous ND segment in the chain. For example,Δω_(N)>√{square root over (2)}Δω₀, where N is the ND segment numberfurther provided

$L_{nl}^{({ND})} < \frac{L_{D}^{({ND})}}{2}$

and the ND segment length (L_(ND)) satisfies L_(ND)≥2L_(nl) ^((ND)).This bandwidth increase is shown graphically in FIG. 1(B) showing anexample numerical result for such a chain.

In general, as long as L_(nl) ^((ND))≥L_(D) ^((ND)) our calculated lowerbound of the spectral bandwidth ratio in each ND segment varies from2.8, when L_(nl) ^((ND))→0 to 1.1 when L_(nl) ^((ND))=0.8L_(D) ^((ND))(provided L_(ND)≥2L_(nl) ^((ND))).

FIG. 2(B) displays the lower bound ratio across this range. Thus, withinthe range, L_(nl) ^((ND))≤0.8L_(D) ^((ND)), Δω_(N)>1.1^(N)Δω₀ and islower bound by an exponential function.

In fact, it outperforms spectral generation in the ideal but physicallyunattainable case without dispersion where the bandwidth growthconverges to a linear increase with propagation, with a sufficientnumber of ND segments. The more physically relevant uniform dispersioncase saturates to a constant bandwidth past a certain L_(ND) length(this length is labelled as L_(sat) ^((ND))), so methods according tothe present disclosure will always substantially outperform this case.In fact, if the ND segment length is chosen to be equal or greater thanL_(sat) ^((ND)), our method according to the present disclosureoutperforms the uniform dispersion case within the first ND segment.

FIG. 2(A) is a plot illustrating the comparison of our method accordingto the present disclosure with these two cases in an example calculationusing experimentally relevant parameters. More specifically, FIG. 2(A)is a plot showing the comparison of the spectral development in each NDsegment along the propagation direction of the ND SCG chain with anequivalent length case of just the ND waveguide wherein dispersion isnot present but nonlinearity remains and the equivalent length casewherein there is only a continuous length of the ND material with bothdispersion and nonlinearity. Note that the dispersion chosen isconsidered to be within a standard range for step-index fibers and isthus not a negligible value according to aspects of the presentdisclosure.

FIG. 2(C) shows graphically the comparison of this example calculationwith the lower bound spectral ratio estimation. More particularly, FIG.2(C) is a plot showing the bandwidth increase ratio at the end of eachND segment (with respect to the previous segment) wherein the lowerbound calculation is shown and the ratio of the nonlinear to dispersionlength of at the start of each progressive ND segment is shown accordingto aspects of the present disclosure.

We note that the power of this lower bound estimate is not only to showthe spectral bandwidth increases greater than an exponential functionwithin a certain domain of interest but it can be used as a tool in thedesign of these chains to obtain the nonlinear lengths needed toguarantee a certain bandwidth increase dynamic (and thus, a certain endbandwidth). However, the estimate itself is strict and for L_(nl)^((ND))>0.8L_(D) ^((ND)) it is lower than one (e.g., shown in FIG.2(B)). While it is still true in the sense of a lower bound it becomesphysically meaningless, since the spectrum should always increase underthe conditions of the ND SCG chain. For L_(nl) ^((ND))≥L_(D) ^((ND)), itis expected that spectral increases will still happen albeit not boundedby one exponential function in the entire domain. This is shown in theexample case of FIG. 2(C). In fact, as shown in FIG. 2(A) and FIG. 2(C),the alternating waveguide structure overcomes the case where there is nodispersion and just SPM in later ND chain segments when L_(nl)^((ND))≥L_(D) ^((ND)). This will be demonstrated experimentally at alater point of this disclosure.

To make the above more precise, FIG. 2(C) shows that the bandwidth ratioof subsequent ND segments in the chain remains substantially higher thanthe lower bound estimate and higher than 1.4 even for L_(nl)^((ND))>>L_(D) ^((ND)). Furthermore, the ratio stays greater than 1.1even for L_(nl) ^((ND))≈7L_(D) ^((ND)). As well, the chain outperformsthe no dispersion case (shown in FIG. 2(A)) past ND segment numberswhere L_(nl) ^((ND))>L_(D) ^((ND)). This numerical example then showsthat the ND SCG chain can also work in the limit of low peak intensitywhere dispersion dominates over the nonlinearity of the material. Thus,the ND SCG chain has the additional advantage that it overcomes spectralclamping for low peak intensity laser inputs and thus, SCG can begenerated at even these low peak intensities when the nonlinear lengthis far greater than the dispersion length. Thus, the alternating chainnot only can advantageously overcome ND spectral clamping but can makeSCG accessible to the low peak intensity laser regime.

Description of AD SCG and Mixed Case

Another important case is when the main contribution to spectralbroadening through self-phase modulation occurs in the anomalousdispersive segments in the chain (i.e., an AD SCG chain). In such asituation, nonlinear temporal compression takes place in the ADsegments, and due to the rising peak intensity and reduced duration, SPMexpands the spectral bandwidth. However, past a certain propagationlength in the AD segment either the pulse moves past its temporal focus,inverting the direction of its temporal chirp and leading to SPMspectral narrowing or soliton formation takes place and ceases anysubstantial coherent spectral bandwidth increase (i.e., clamps thespectrum). Thus, the length of each AD segment is chosen such thatbefore these two processes take place the pulse enters an ND segmentwhere it is temporally defocused and chirped. After the ND segment, inthe subsequent AD segment, the pulse is not at its temporal focus nor isit close to the short duration, high peak intensity profile needed tocouple into solitons. Consequently, spectral generation takes place asthe pulse is temporally compressing from its dispersed chirped profile.Again, before it compresses to the point where soliton fission ortemporal chirp inversion takes place, the AD segment is terminated. Inthis manner, spectral generation can continue in an unclamped fashion inthe chain just by the addition of AD-ND cycles.

Since, the material dispersion increases SPM spectral broadening in theAD SCG process before spectral clamping occurs, AD SCG has a higherspectral bandwidth than ND SCG, where material dispersion always worksto counter SPM spectral broadening. Thus, the AD SCG chain variant mayrequire less chain cycles to generate a desired spectral bandwidthrelative to the ND SCG chain counter-part. As well, this methodgenerates SCG even when the input pulse energy is below the fundamentalsoliton energy which is needed to initiate SCG in conventional setups.Therefore, as in the ND SCG chain variant of the method, the AD SCGchain not only overcomes AD spectral clamping processes but renders SCGaccessible to low pulse energy regimes that are below the cut off neededfor SCG in conventional AD SCG waveguides.

Note that the last case is that spectral generation is substantiallydone in all segments and they (ND or AD segment) mutually prevent eachother's spectral clamping mechanisms (i.e., AD and ND SCG spectralclamping mechanisms).

Experimental Setup and Results

To demonstrate systems, methods, and structures for SCG experimentally,a fiber-based wave guiding was chosen to realize a ND SCG chain, becausefibers enable easy control of the length of the segments to optimize theSCG. Additionally, the fibers can be joined relatively easily using acommercial splicer and cleaver. Accordingly, fibers were chosen suchthat the ND SCG chain case could be quickly and convenientlydemonstrated experimentally.

Experimental Setup: The illustrative experimental setup, shownschematically in FIG. 3, comprises a source for generating ultra-shortoptical pulses which are injected into a chain of fiber segments forSCG. The source includes a commercially available, passively mode-lockedErbium doped fiber laser, amplifier and a temporal compressor system.

Operationally—and for the purposes of our experimental purposes and inno way limiting the scope of our disclosure—pulse parameters of a pulseentering the fiber chain are a 74 fs FWHM pulse duration, 50 mW averagepower at a 79.9 MHz repetition rate, at a central wavelength of 1560 nm.The power coupled into the fiber was 35.6 mW (446 pJ pulse energy).

Segments of standard single-mode doped-silica step-index optical fiber(Corning Hi1060flex for ND, Corning SMF28 for AD) were used. This hasthe benefit of providing well-characterized dispersion properties, seeFIG. 4, and nonlinear properties, which makes numerical modeling andcomparison with experimental data more reliable. These specific singlemode fibers were chosen due to their sign-inverted second orderdispersion relative to each other in the wavelength region of the pumplaser, the high nonlinear coefficient of the ND fiber, and because lowsplice loss can be achieved between them.

As may be observed, FIG. 4 is a plot illustrating second-orderdispersion vs. wavelength of experimentally used AD and ND fibersegments in which the vertical dotted lines indicate the zero dispersionwavelengths of the AD (1.31 μm) and ND (1.83 μm) segments according toaspects of the present disclosure.

For the first ND segment, we obtain L_(nl) ^((ND))≈4.1 cm and L_(D)^((ND))≈10.1 cm, satisfying

$L_{nl}^{({ND})} < {\frac{L_{D}^{({ND})}}{2}.}$

However, it is not guaranteed that this inequality is maintained for allsubsequent ND segments since L_(D) ^((ND)) reduces faster withdecreasing pulse duration. In fact, in our experiment, L_(nl)^((ND))>L_(D) ^((ND)) past the 3^(rd) ND segment, however, it is shownin the results that spectral bandwidth increase still takes place.

Experimental Procedure: The experiment was performed by starting with a25 cm piece of the ND fiber, and measuring the spectrum from its outputusing an OSA. The length was shortened (cut) until a slight reduction ofthe spectral width became noticeable (e.g., at the −30 dB level). Thisensures that the fiber length is within the length where the spectralgeneration is ongoing and not clamped. Past this length, the spectralgeneration clamps (i.e., it is negligible with magnitudes less than −30dB), as discussed above due to the dispersive temporal defocusing.

Shortening the fiber to this length disrupts further pulse defocusingthus minimizing phase contributions from higher order dispersion,however, without disrupting the spectral generation. It is important toremove such phase contributions to achieve better pulse compression inthe following AD segment because, in our demonstration, the AD fibercannot completely compensate for the high order dispersion of the NDfiber and thus cannot compensate for this.

Next, a 20 cm piece of AD fiber is spliced to the ND fiber and the pulseduration is measured with an intensity auto correlator (APE PulseCheck). The fiber shortened until the autocorrelation trace (AC)indicates a minimum pulse duration, i.e., that the temporal focus liesat the output facet. The procedure is then repeated with the next pieceof ND fiber and so forth.

Results and Discussion

Spectral and Temporal Evolution of ND SCG Fiber Chain: The experimentalresults are shown in FIG. 5, which is a plot illustrating measured powerspectrum obtained from supercontinuum generation in a segmented chainfiber waveguide in which—for comparison—the measured spectra obtainedwith the same length of normally dispersive (ND) fiber and anomalousdispersion (AD) fiber are displayed as well as obtained with the samepulse input parameters, also a numerical simulation, according toaspects of the present disclosure.

As may be observed and understood by those skilled in the art, asignificant increase of the spectral bandwidth is realized—as comparedto fibers with equal length of non-segmented ND and AD fiber. Also,shown is the result of theoretical modelling based on numericallysolving the generalized nonlinear Schrodinger equation. The theoreticalprediction supports the experimental data, namely, that there is a largebandwidth enhancement for the ND SCG alternating chain. FIG. 5 alsoshows numerically and experimentally that, compared to the input pulse,there was negligible spectral generation in the AD fiber, proving thatthis type of fiber chain is operating within the regime of the ND SCGdominated chain case, i.e., spectral generation predominantly occurs inthe ND segments.

At this point those skilled in the art will readily appreciate thatsupercontinuum generation according to aspects of the present disclosureresulting from alternating dispersion as now taught and disclosed isrealizable, practical, and surprisingly effective.

These results provide, to our knowledge, the first demonstration of thisnovel method of SCG: From the substantial relative bandwidth increase ofthe spectrum obtained with the chain versus the clamped spectrum of theND fiber of the same length, this chain fiber system advantageouslycircumvents the spectral clamping that occurs in ND fiber SCG throughloss of peak intensity.

For example, the e⁻¹ spectral width of 233 nm for the chain is a factor1.7 wider than with the ND fiber and a factor of 2.7 than with the ADfiber. This spectral enhancement was obtained with an additional loss of49% within the fiber chain over the reference fibers, thus making thissignificant enhancement even more substantial since it is effectivelyobtained at half the available power.

The experiment also demonstrated that the spectral bandwidth growth cantake place for L_(nl) ^((ND))>L_(D) ^((ND)) even at early segments inthe ND SCG chain (i.e., at the 3^(rd) ND segment in the fiber chain).

Moreover, of considerable importance is that the experiment demonstratedthat—provided they have opposite sign—the alternating ND-AD dispersionparameter profiles need not be strict to a specific arrangement withrespect to higher order dispersion parameters (i.e., greater than secondorder). Rather, the chain is robust to deviations in the dispersionparameter shapes. This is elaborated more in the next paragraph and thenext section.

FIG. 6(A) is a plot illustrating relative spectral energy density (dB)vs. wavelength (μm) for an output spectrum measured behind each NDsegment in the chain according to aspects of the present disclosure; andFIG. 6(B) is a plot illustrating relative pulse intensity (color coded)and temporal shape (Fs) vs. propagation distance (cm) vs. time (fs) inwhich the time coordinate is taken in a frame moving with group velocityaccording to aspects of the present disclosure.

With simultaneous reference to those figures, it may be understood thatFIG. 6(A) shows a more detailed set of experimental data, i.e., thespectral development while FIG. 6(B) shows theoretical data of thetemporal development of the SCG vs propagation through the growingnumber of these fiber segments. Furthermore, it can be seen that thespectral bandwidth grows stepwise with each ND segment (see, e.g., FIG.6(A)) while the pulse FWHM duration oscillates between about 30 fs and175 fs (see, e.g., FIG. 6(B)) across the propagation coordinate. Bothdevelopments confirm the proper working of the novel method according toaspects of the present disclosure.

It was also experimentally verified that the last AD segment was able tocompress the pulses to an auto correlated value of 46 fs (˜33 fs) FWHMwhich is a substantial additional advantage to the alternating chain SCGand of potential use to practical SCG experiments; at the output of thechain, if terminated by an AD segment, the SCG pulse is already in atemporally compressed form. To our knowledge, we have not found an allfiber SCG system that compresses the output pulse to sub 50 fs durationsat this central wavelength with these fibers exhibiting unmatched inmagnitude higher than second order dispersion coefficients (i.e.,unmatched higher order dispersion).

We note that the last (fourth) ND segment provided a e⁻¹ spectralbandwidth ratio of 1.28 relative to the previous segment. This exceedsexpectations given that L_(nl) ^((ND))>>L_(D) ^((ND)). However, at thisND segment number the spectral increase starts to slow. Ultimately, thespectral increase in subsequent segments in this fiber chain renditionare limited due to the loss of peak intensity from uncompensatedspectral phase and cumulative splice losses.

In a practical implementation of the ND SCG chain, the dispersionparameter profiles of the two segments do not have opposite signs acrossthe entire spectral range of relevance. Past a certain bandwidth,uncompensated spectral phase arises because the dispersion parameter, Dof the ND fiber and AD fiber has the same sign. This ultimately createsan increasing temporal separation for radiation in this spectral region(temporal walk-off), a continuous temporal broadening of this radiationand a lowering of the overall temporal peak intensity. This limits notonly spectral generation in this region but the overall spectralgeneration.

We note that this is a technical limitation in our experiment.Specifically, because of this, it is expected that the spectralgeneration should be clamped, near the two zero dispersion wavelengths(ZDWs) of the AD and ND segments at 1.31 μm and 1.83 μm (shown in FIG.4) i.e, the largest possible bandwidth at the e⁻¹ level is the rangebetween the two ZDWs. When these endpoints are approached, the spectralgrowth in additional ND segments would cease.

As well, within the spectral range where the signs of D are oppositebetween the ND-AD segments, spectral phase build up still occurs. Thisis because the AD fiber segments introduce higher than second orderdispersion (the ND segments higher order dispersion contributions areless substantial, as discussed in the next section). This results in anuncompensated spectral phase after each ND-AD segment cycle that buildsup within the range between the ZDWs. This also results in the loweringof the peak intensity and temporal walk off into sub-pulses (centered atdifferent central wavelengths). However, this occurs after many chainsegments, being a higher order dispersion effect, and it may be that thechain is rather resilient to this process (see next section). Evidenceof these processes are highlighted in FIG. 6(B).

The impact of Higher Order Dispersion and Ideal Dispersion Parameters:The impact of higher order (i.e., higher than second order) spectralphase contributions due to SPM contributes less to its overall spectralphase contribution. The second order phase contribution of SPM dominatessince higher order contributions mainly arise from the spectralcontributions of the wings of the temporal pulse, where the SPM chirpdecreases back to the original carrier frequency of the pulse (here weassume close to Gaussian pulses). As such, these contributions can betreated as negligible due to the low amount of energy captured in thewings of the pulse relative to the main portion (within the e⁻¹ temporalwidth).

As will be readily appreciated by those skilled in the art—and ofparticular advantage for systems, methods, and structures according toaspects of the present disclosure—the AD segments need only compensatefor this second order phase contribution (which is chirped in the samedirection as the ND dispersion phase function and opposite to the ADdispersion phase function). This can easily be accounted for byadjusting the length of the AD section thereby matching the magnitude ofits group delay dispersion (GDD) coefficient.

We note that the higher order dispersion of the ND segment can beeffectively ignored in ND segments where large SPM spectral broadeningoccurs, since the dispersive phase contribution is continuouslystretched over the increasing spectral bandwidth. If the ND segmentlength is discontinued (too short) before spectral clamping in thatsegment occurs, the dispersive phase contributions are effectivelydivided over a larger bandwidth. This would have the effect that the GDDintroduced by the ND segment is lower and its higher order phasecontributions even lower. Thus, in the beginning chain cycles, thespectral generation is robust to the higher order dispersion of the NDsegment (all that counts is that the second order dispersion coefficientbetween the two segments has opposing signs for pulse compression).Therefore, since the dominant higher order phase contributions are fromthe higher order dispersion of the AD segment, a group velocitydispersion (GVD) parameter profile that has minimum higher orderdispersion is ideal (i.e., flat).

When spectral generation in later ND chain segments becomes lessdominant (i.e.,L_(nl) ^((ND))>L_(D) ^((ND)) or when the length of the NDsegments are larger than the spectral saturation length, it is thenideal to have mirror reflected dispersion parameter (or GVD) profilesabout the spectral-axis between the AD and ND fiber segments (determinedto an arbitrary constant that can be set by the length of the ADsegment).

We note however—in the experiment—the dispersion parameter profiles ofthe AD and ND fiber segments are neither spectral-axis mirror reflectedprofiles of each other nor does the AD dispersion parameter profilecorrespond to a flat GVD along the spectral range of interest (in fact,it deviates considerably from this). Yet it was experimentally observedthat the alternating chain had a significant spectral enhancementrelative to the reference fibers. As well, a pulse duration of 33 fs wasexperimentally verified at the last AD segment of our fiber chain. Thistemporal compression is unprecedented with such fiber segments ingeneral and thus verifies convincingly that the chain is robust to thespecific dispersion parameter shapes (provided the signs alternate).

This may be explained by the fact that while the profiles are far fromideal, the opposing dispersion parameter signs (and that the segmentlengths vary along the chain) render that some SPM generated spectralcomponents can “orbit” around the nonlinearly interacting main pulse (orsub-pulses) and at positions along the propagation coordinate overlapagain with the main radiation (perhaps after a set amount chain cycleslater in the chain). Thus, they may then still contribute to spectralgeneration, through XPM with the main pulse, resulting in spectralbandwidth generation, and/or that these spectral components shift theirfrequencies to places along the dispersion curve where the spectralphase is better compensated between the alternating segments. Thisorbital dynamic of these spectral components results in the peakintensity being maintained for a larger amount of chain segments andless affected by uncompensated spectral phase along the propagationcoordinate and an ongoing spectral generation. This results in the chainbeing rather robust to the specific shape of the component segmentdispersion parameter profiles and just strict to the fact the dispersionsigns alternate between these segments.

Of particular importance from the results of the experiment is that themethod is robust to these higher than second order phase processes ascan be seen by the large spectral enhancement and the temporal pulsecompression achieved, but nevertheless these processes, especially thehigher order dispersion of the AD segments, can influence the spectralgeneration (for example the dynamics of the bandwidth increase ratio)after many chain cycles.

CONCLUSIONS

We have now disclosed and presented a novel approach towards wave guidedsupercontinuum generation which overcomes fundamental limitations ofcurrent methods. Via alternating the waveguide dispersion between normaldispersive and anomalous in segments of suitable length along thepropagation direction spectral clamping in SCG can be overcome, whilemaintaining coherent generation. As well, SCG can be extended to lowpeak powers, arbitrarily lower than what is conventional using thisapproach.

We have explored and discussed in detail the case where SCG occurspredominantly in the normally dispersive segments both theoretically andexperimentally. We found that under ideal conditions, even in thepresence of typical waveguide (fiber) dispersion the spectral bandwidthenhancement can exceed the case where there is no dispersion. We alsoderived lower bound estimates that can aid in the design of suchalternating waveguides. We demonstrate the novel approach experimentallyusing segments of standard normal dispersion and anomalous dispersionfiber spliced in a chain. We generated a SC spectrum with substantiallyhigher bandwidth than with the equivalent length of fiber using onlynormal dispersion or anomalous dispersion. We also found that the fiberchain is rather robust to higher than second order dispersion of thesegments and a high spectral enhancement and pulse compression can stillbe achieved.

We note that our calculations and/or experiments that we have performedindicate that AD segment length converges to a fixed length withincreasing chain cycles. Since the ND segment length can be configuredto be constant this means that for alternating segment chain cyclessufficiently large, the segment lengths would approach a periodicarrangement. As will be understood and appreciated by those skilled inthe art, this makes systems, methods, and structures according to thepresent disclosure compatible with repeated nonlinear generation as in aresonator. For example—and in no way limiting—one could configure asystem in which an end of the alternating segment chain is looped backto a portion of the chain at which periodic convergence of segmentlengths begin. Alternatively, if one accepts the reduced spectralgeneration per chain segment that would be present in a beginningportion of the chain with a periodic structure, one could use the entirechain as an alternating dispersion resonator for controlling Kerr-combgeneration in integrated optical resonators.

Finally, we note once more that systems, methods, and structuresaccording to aspects of the present disclosure may advantageously takeadvantage or or otherwise employ silicon photonics technologies,methodologies, and/or materials and be included into integrated systems,and structures. FIG. 7(A)-FIG. 7(E) are schematic diagrams ofillustrative waveguide configurations providing SCG of optical pulsesthat may advantageously and illustratively implemented in integratedwaveguide structures employing contemporary processes and materialsaccording to aspects of the present disclosure in which: FIG. 7(A) is afirst case illustrative configuration; FIG. 7(B) is a second caseillustrative configuration; FIG. 7(C) is a third case illustrativeconfiguration; FIG. 7(D) shows illustrative parameters of waveguidestructures; a plot illustrating relative spectral energy density (dB)vs. wavelength (μm) for an output spectrum measured behind each NDsegment in the chain according to aspects of the present disclosure;FIG. 7(E) shows cross-sectional views of illustrative waveguides;—allaccording to aspects of the present disclosure.

At this point, while we have presented this disclosure using somespecific examples, those skilled in the art will recognize that ourteachings are not so limited. Accordingly, this disclosure should beonly limited by the scope of the claims attached hereto.

1. A waveguide structure for supercontinuum generation CHARACTERIZED BY:alternating segments of normal dispersion (ND) waveguide segments andanomalous dispersion (AD) waveguide segments along a length of thewaveguide structure.
 2. The waveguide structure of claim 1 FURTHERCHARACTERIZED BY: the alternating segments configured such that spectralgeneration of optical pulses traversing the structure is effected in theND segments and spectral bandwidth increase in the AD segments is lessthan or equal to 10% relative to spectral bandwidth increase in thepreceding ND segment.
 3. The waveguide structure of claim 2 FURTHERCHARACTERIZED BY: the absence of spectral clamping of the opticalpulses.
 4. The waveguide structure of claim 1 FURTHER CHARACTERIZED BY:the alternating segments configured such that spectral generation ofoptical pulses traversing the structure is effected in the AD segmentsand spectral bandwidth increase in the ND segments is less than or equalto 10% relative to spectral bandwidth increase in the preceding ADsegment.
 5. The waveguide structure of claim 4 FURTHER CHARACTERIZED BY:the absence of spectral clamping of the optical pulses.
 6. The waveguidestructure of claim 1 FURTHER CHARACTERIZED BY: the alternating segmentsconfigured such that supercontinuum spectral generation of opticalpulses traversing the structure is effected in both AD and ND segmentswherein the pulses are temporally compressed in one of the segment typesand temporally expanded in the other one of the segment types andspectral clamping is absent in both segment types and where spectralbandwidth increase in neighboring AD and ND segments are both more than10%.
 7. The waveguide structure of claim 1 FURTHER CHARACTERIZED BY: thelengths of the segments are aperiodic such that their lengths are notrepeating over a portion of the waveguide structure length.
 8. Thewaveguide structure of claim 1 FURTHER CHARACTERIZED BY: the lengths ofthe segments are periodic such that their lengths repeat for every NDand AD segment of the waveguide structure.
 9. The waveguide structure ofclaim 2 FURTHER CHARACTERIZED BY:${L_{nl} \equiv \frac{1}{\gamma \; P_{o}}},{{L_{D} \equiv \frac{t_{0}^{2}}{\beta_{2}}};}$wherein t_(o) is the transform limited pulse duration (FWHM intensity)of an optical pulse applied at the input of the AD or ND segment, P_(o)is the input peak power,${\gamma = {k_{o}\frac{n_{2}}{A_{{eff}\;}}}},$ is the nonlinearcoefficient, where k_(o) is the free-space wavenumber, n₂ is the Kerrnonlinear refractive index, A_(eff) is the effective mode area in thesegment at the central frequency, and β₂ is the AD or ND segmentdispersion coefficient.
 10. The waveguide structure of claim 1 whereinthe alternating waveguide segments comprise optical fiber.
 11. Thewaveguide structure of claim 1 wherein the alternating waveguidesegments comprise integrated, planar optical waveguide structures. 12.The waveguide structure of claim 1 wherein the alternating waveguidesegments are arranged linearly.
 13. The waveguide structure of claim 1wherein the alternating waveguide segments are arranged non-linearly.14. The waveguide structure of claim 1 wherein at least a portion of thewaveguide segments are arranged in a ring.
 15. The waveguide structureof claim 1 wherein the alternating segments are configured such that thespectral bandwidth of optical pulses traversing the waveguide structureare increased and the spectral bandwidth increase in a succeeding ADsegment is less than 10% relative to the spectral bandwidth increase inthe preceding ND segment.
 16. The waveguide structure of claim 1 whereinthe alternating segments are configured such that the spectral bandwidthof optical pulses traversing the waveguide structure are increased andthe spectral bandwidth increase in a succeeding ND segment is less than10% relative to the spectral bandwidth increase in the preceding ADsegment.
 17. The waveguide structure of claim 1 wherein the alternatingsegments are configured such that the spectral bandwidth of opticalpulses traversing the waveguide structure are increased and the spectralbandwidth increase in both AD and ND segments is more than 10% relativeto the spectral bandwidth increase in the preceding segment.
 18. Asystem for supercontinuum generation comprising: an optical source inoptical communication with a waveguide structure; the waveguidestructure including alternating segments of normal dispersion (ND)waveguide and anomalous dispersion (AD) waveguide along a length of thewaveguide structure, said waveguide structure configured to alternatethe sign of a dispersion profile along the length of the waveguide; suchthat light pulses emitted from the optical source undergo a spectralbroadening as it propagates the length of the waveguide structure. 19.The system of claim 18 wherein the alternating segments configured suchthat supercontinuum spectral generation of optical pulses traversing thestructure is predominantly effected in one of the segment types selectedfrom the group consisting of ND segments and AD segments; and thewaveguide segments are of a particular construction type selected fromthe group consisting of optical fiber and planar optical waveguide. 20.A method of supercontinuum generation comprising: directing a lightpulse into an optical waveguide structure; spectrally broadening andreshaping the light pulse by repeatedly alternating the sign of thedispersion spectrum along a propagation coordinate of the waveguidestructure, said waveguide structure including alternating segments ofnormal dispersion (ND) waveguide and anomalous dispersion (AD) waveguidealong a length of the waveguide structure; emitting spectrally broadenedlight pulses from the waveguide structure.
 21. The method of claim 20wherein the alternating segments are configured such that supercontinuumspectral generation of optical pulses traversing the structure ispredominantly effected in one of the segment types selected from thegroup consisting of ND segments and AD segments; and the waveguidesegments are of a construction type selected from the group consistingof optical fiber and planar optical waveguide.